Depends which "left" we're talking about. Depending on who you talk to, when people say "the left" they can mean neoliberals, liberals, centrists, Democrats, centre-leaning Republicans, anarchists, Communists, Socialists, Marxist-Leninists, or just a pick and mix of all of the above. To be fair, the same can often be said when people use the term "the right".
I don't consider the modern Democratic party to be actually politically leftwing, but understand and accept that the majority of people in America, when they refer to "the left" often mean the Democratic party and anyone to the left of it.